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Chapter 1

INTRODUCTION

Nowadays, energy conservation and safety have become the main directions for

vehicle research and development. Within these measures of oil saving and emission

reduction, the weight reduction of vehicle itself has the most significant effect. So active

research is currently being devoted to the development of highly innovative designs involving

lightweight materials, such as high strength steel, aluminum or magnesium alloys, and

metallic or polymeric foams. To meet the demand of vehicle safety and weight reduction,

during the past decades, many research works have been carried out in energy absorption

characteristics of thin-walled structures, including empty thin-walled columns and foam-

filled thin-walled members.

Fig 1.1

Bumper beams are one of the important structures in passenger cars. For which we

need to have careful design and manufacturing in order to ensure good impact behavior. The

new bumper design must be flexible enough to reduce the passenger and occupant injury and

stay intact in low-speed impact besides being stiff enough to dissipate the kinetic energy in

high speed impact. The bumper beam is the key structure for absorbing the energy of

collisions. Since, this is energy absorbing structure suitable impact strength is the main

requirement for such a structure

Thin-walled columns have a high energy-absorption capabilityand therefore have

played an important role in vehicle crashes.Most of the frames in modern vehicles are made

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from thin-walledsections. Tubes absorb the impact energy through materialdeformation

during crushing. The collapse of a tube has twoprimary modes, axial and bending, but during

an actual crashevent, the tube is subjected to either pure axial or bendingcollapse, but rather a

combination of the two modes. If the tubeexperiences global bending instead of axial

crushing, the energyabsorption will be lower, and both moments and axial forceswill be

transferred to the rest of the structure

Crashworthiness studies devote a great deal of attention to thebehavior of thin-walled

structures, which have been widely usedas load bearing structures as well as energy absorbers

in engineeringpractices such as in automobile and aeronautical applications[1].The increasing

interest in safety and crashworthiness of structures has led to a comprehensive research on the

crashing responsesof thin-walled tubes with different cross sectiongeometries analytically

[2,3], numerically [4,5] and experimentally[6,7]. Optimization studies on thin-walled

structures for the crashworthinessdesign have also been carried out [8–10]. Studying

thecrashworthiness of thin-walled tubes subjected to bending is relativelynew, because to

date the investigations have mainly been focusedon the collapse of thin-walled circular tubes

under axialloading [11–14].

The crash box located between bumper and side rails protectspassengers and

expensive vehicle components by absorbing initialkinetic energy in a frontal vehicle crash

event by ensuring a lowplastic flow stress level on the auto-body frame

Energy absorbers are often part of the car structure to protect passengers and the

structure itself during impact. One type of energy absorber is the crash box, which is

connected to thebumpers, situated in the front and rear end of the body structure. The crash

box is designed absorb energy at low speed impacts. Its purpose is to control the initial

kinetic energy during impact, and at the same time avoid permanent deformations in the rest

of the car body by keeping the force levels sufficiently low. The absorption of energy is

controlled by the plastic work in thecrash box, which is given by the area below the

forcedisplacement curve.

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Fig 1.2 Bumper beam

Experienced automotive engineers design functional components in the context

oftheir surrounding elements. For example, a bumper should not be stronger than the

structure it isintended to protect. Likewise, the stiffness of the vehicle structure to which the

bumper is mounted contributes to the total elastic displacement of the bumper surfaces, and

hence to itsenergy absorption.

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Chapter 2

LITERATURE REVIEW

The literature review of Energy absorbing is explained as follows. The author

JavadMarzbanrad, Mehdi Mehdikhanlo,AshkanSaeedi Pour, in their paper they have

simulated a theory about the axial crushing of steel and aluminiumtubes between 2

parallel plates subjected to impact dynamicaxial loading was investigated. A

nonlinear finite element model was developed and analyzed with LS-DYNA inthis

simulation. Verification was done through comparison with some experimental results

in a steel square tube. Good agreement was observed between the FEM force histories

with those obtained from experimental results. Typical deformation histories for 3

sectional types (square, circle, and ellipse) were studied and presented. Itwas

concluded that the elliptic tubes absorb more energy during collisions. The effects of

width and thicknesswere also investigated. It was concluded that the energy

absorption may be increased about 22% with widthenhancement of 66%, showing that

the energy absorption would be one third of the width increase. Relatedto thickness,

the amount of energy absorption will be more with increasing thickness for smaller

section tubes. Energy per weight absorption during the collision of 2 metals (steel and

aluminium) was also calculated andcompared. The results showed that the amount of

energy absorption per weight of steel tube was about 4.5times greater than the

aluminum tube for all 3 sections, square, circle and ellipse. However, the square

section and then the circular section of the steel tube absorbed energy per weight more

than the elliptic section of the aluminum tube, respectively [1].

The author A.AlaviNian,M. in their paper they have simulated a theory about

the mechanical behavior of thin-walled aluminum structures with triangular, square,

hexagonal and octagonal sections in simple and multi-cell forms was studied under

quasi- static compression. Samples were loaded using a Santam apparatus and

simulations were done using LS-DYNA code. There was good consistency between

the test data and simulation results. Experimental samples showed lower initial peak

load in comparison with simulations because on the type of connection therefore, their

crushing force efficiency was greater than for the simulated samples. A comparison of

the results showed that multi-cell sections had greater SAE in comparison with simple

sections, especially for triangular geometry. It was shown that the first type of multi-

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cell section, mc-1, was more efficient than the second type, mc-2.Finally, SAE for

mc-1with hexagonal and octagonal geometries was about 120% and 118% greater,

respectively, than for the simple triangular geometry [2].

The author T Børvika , O S Hopperstad

a , A Reyes

a , M Langseth

a G Solomos

and TDyngelandb

in their paper they have simulated a theory about the empty and

foam-filled circular aluminum tubes subjected to axial and oblique quasi-static

loading Tests on tubular columns made of the aluminum alloy 6060-T4 under axial

and oblique, quasi-static loading have been performed. The columns were fixed at one

extremity, while a concentrated force was applied at the other through a rigid collar.

Empty and foam-filled columns were tested for load angles equal to 0, 5, 15 and 30

degrees with respect to the longitudinal direction of the column. The column’s outer

diameter was 80 mm and the thickness was 1.5 mm, while the distance from the point

of load application to the fixed support was 245 mm. The aluminum foam density was

about 0.3 g/cm3. The response parameters were the peak force, the absorbed energy

and the mean crush force, in addition to visual observations of the deformation mode

and fracture. Furthermore, LS-DYNA simulations of the experiments were performed.

The columns were modeled with shell elements, while brick elements were used to

model the aluminum foam core. The aluminum alloy was modeled using an isotropic

elasto-plastic model with isotropic strain hardening. Fracture in the aluminum column

was not considered in the simulations. The aluminum foam was modeled using the

Deshpande-Fleck model. In selected simulations, fracture was assumed to occur at a

critical value of the plastic volumetric strain. The agreement between the

experimental and predicted results was in general good [3].

The author Md. Reyaz Ur Rahimí A.K. Upadhyay K.K. Shuklain their paper

they have simulated a theory about the energy Absorption by Circular Tubes

Subjected to Oblique Loading. The energy-absorbing capability of obliquely loaded

circular thin-walled structural steel tube is studied with different loading angles and

geometric parameters using ANSYS-14. The collapse behavior of tubes is

investigated at loading angles of 00, 50,100 and 150 with respect to the longitudinal

direction of the tube. Parametric studies are carried out in order to assess the effect of

load angle, wall thickness, height and the hole with varying position on energy

absorbing capacity of obliquely loaded steel tubes. In this paper the behavior of the

tubes subjected to oblique load is studied and the response is analyzed at various

lengths, thicknesses, inclinations and effect of hole on it. Paper gives a subsequent

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steps has taken to see understand all the possible effects on tube when loaded

obliquely under certain defined conditions. Initially the tube length effect, thickness

and inclination effect has been observed, than the effect of hole as a buckling initiator

is also presented and finally the best position of the hole to get the higher energy

absorbing capacity is concluded [4].

The author Yong Zhang, Guangyong Sun, Guangyao Li , Zhen Luo , Qing Li

in their paper they have explored a theory about the crashworthiness design for a

special thin-walled structure made of foam-filled squared bi-tubal columns. The

design criteria of specific energy absorption (SEA), peak impact force (Fmax) and

utilization rate (UR) of progressive deformation length were taken into account under

dynamic crushing loading. The Kriging modeling technique was adopted for

approximating the response functions. Firstly, to optimize crashworthiness the genetic

algorithm (GA) and Non-dominated Sorting Genetic Algorithm (NSGA) II were

applied for the single-objective and multi objective optimization, respectively. It is

noted that the optimal result of the single-objective optimization represents a special

point in the Pareto front. From this perspective, the multi-objective optimization

appears more suitable for the crashworthiness design problems that often require

addressing a number of different criteria. Secondly, to compare with the optimized

foam filled mono-tubal column, the multi-objective optimization was also performed

and the results showed that the foam-filled bi-tubal column has a better

crashworthiness than the foam-filled mono-tubal column for the wall thickness

available practically in vehicle engineering. Thirdly, the crashworthiness of empty bi-

tubal column and foam-filler was separated to explore the role of foam-filler in such a

more sophisticated bi-tubal structure. The comparative study demonstrated that the

foam-filled bi-tubal structure is better than the empty bi-tubal column as well as the

sum of two separate components of the empty bi-tubal column and foam-filler as their

own. It is concluded that the optimized foam-filled bi-tubal structure could provide a

better crashworthiness performance than the foam-filled mono-tubal column and

empty bi-tubal column. It can be a potential structural component for vehicle

engineering applications [5].

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Chapter 3

SHAPES, MATERIALS OF TUBES AND ENERGY ABSORPTION

Thin-walled tubes of different geometry and materials have been prevalently used as

collapsible energy absorbers in various kinds of structural applications. Such devices are

designed to collapse progressively for absorbing impact energy in a controlled manner and

converting kinetic energy in to [plastic strain energy in impact situations. There are various

types of sections of tubes they are listed below,

Circle

Square

Triangular

Ellipse

3.1 Circular Tube:

A circular tube is representing an efficient and light crash absorber under loading

condition. In addition, circular tubes under compression are reported to be the most prevalent

components in energy absorbing systems since they provide reasonably constant operating

load.

3.1.1 Advantages:

1. A general observation tells us that circular tube has better energy absorption

performance.

2. It represents an efficient and light crash absorber under axial loading.

3.1.2 Disadvantages:

1. When its length is greater than critical length, it deforms in a global Euler

buckling mode, which is an inefficient mode for energy absorption and thus

needs to be avoided in crashworthiness applications.

2. The crush and energy absorption response of circular tubes are significantly

affected by varying geometrical, material and loading parameters.

3.2 Square Tubes:

The deformation mode of square tubes is very different to circular tubes, though the

general characteristics are similar. A rectangular cross section showed the best

crashworthiness in a full car model crash test involving a bumper, crash boxes, front side

members, and sub-frames.

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3.2.1Advantages:

1. Showing great potential for sustaining impact loading.

2. In comparison with circular tube, the actual static crushing load is about 15% smaller

for a square tube.

3.2.2 Disadvantages:

1. It is having problem of global bending collapse mode.

2. Unstable

3.2.3 Solution over global bending problem:

To control an unstable collapse, EL-Hage et al. (2005) proposed a triggering

mechanism (chamfer/tapered) at the end of square tubes in order to control the folding

initiation load and influence the crush stability without affecting the mean crushing load

significantly. It showed that a tapered trigger section at the end of the column may minimize

the crush instability, thereby avoiding global bending.

3.3 Materials of Tubes:

There are following types of materials are used for manufacturing of tubes,

Steel

Aluminum

Composite

3.3.1 Steel:

As shown in table.3.1 absorbed energy Eabsorbed energy increases when one pair of

holes is introduced to the plain tube; this increase will be more as the size of the discontinuity

increases. Pmax seems to be regardless of hole size and number of the holes in steel tubes.

CFE and Pmean are following same trend as Eabsorbed energy. CFE has maximum value at

sampleSt-2B and minimum value at sample St-6S, therefore the sample with only one pair of

discontinuities of small size acts more effectively in absorbing crush energy. Simulation

could truly predict the behavior of the samples in experimental situation since they are nearly

following same pattern in load-displacement

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Table 3.1 Values of Absorbed Energy, Maximum Load, Mean Load and CFE for Steel

samples subjected to quasi-static crushing test.

3.3.2 Aluminum:

In table.3.2 absorbed energy value is shown for each sample. Also Pmax and Pmean

for each one of the graphs are given; adding discontinuities of any size seems to have no

effect on Pmax since it increases in some cases and decreases in some others without any

order. Eabsorbed energy increases as a hole is introduced to a plain tube regardless of hole

size and it tend to decrease afterwards by adding more holes while small size discontinuities

are more effective in raising up the amount of Eabsorbed energy.

Table 3.2 Values of Absorbed Energy, Maximum Load, Mean Load and CFE for Aluminum

samples subjected to quasi-static crushing test

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3.3 Comparison between Aluminum and Steel Material:

Due to physical characteristics of steel its energy absorption capacity is remarkably

higher than energy absorption capacity of aluminum; in the other word steel needs more

energy to deform under compression. This fact is shown in Figure 3.5

Fig 3.5 Comparison between energy absorption capacity of aluminum and steel

Although both aluminum and steel show same trend in energy absorption capacity,

they behave differently when the size of the holes increases; steel needs more energy to

deform for samples with bigger size holes than ones with small size through-hole, on the

contrary aluminum uses less energy to deform when the size of the through-holes are bigger.

Due to results shown in tables 3.1 and 3.2, maximum and minimum CFE in aluminum

happens at samples Al-2B andAl-12B respectively while in steel, samples St-2B and St-6S

are at maximum and minimum of Crush Force Efficiency.

Moreover the range of Pmax is higher in steel than aluminum because of

characteristic differenced of these two metals.

3.4Types of Loading:

A number of analytical models for predicting the mean crushing load of progressive

folding of such tubes have been developed under axial quasi static and impact loading

conditions.

3.4.1a Quasi static and impact loading:

The collapse response and energy absorption capability of circular tubes under quasi

static and impact loading with varying parameters namely wall thickness and tube diameter.

It was found that the energy absorption capacity of tubes in impact tests is higher by about

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1.56-12.3% than quasi static tests, whereas the increase in the initial peak load is between

14.33-40.25%. Moreover, an important finding is that both crush load and energy absorption

capacity increase with increasing thickness and diameter.

3.4.1b Axial Loading:

Circular tube when subjected to an axial load, a circular tube collapses in an efficient

manner when it displays stable progressive collapse and deforms in the axisymmetric ring,

non-axisymmetric or mixed mode. The collapse mode depends primarily on the ratio of

diameter to thickness (D/t), the ratio of length to diameter (L/D) and the material of tubes. In

general, thicker tubes deform via an axisymmetric mode whereas thinner tubes deforms in an

non-symmetrical mode. Figure 3.1 shows typical collapse mode of circular tube under axial

loading.

Fig 3.1 Typical collapse modes of circular tube under axial loading

3.4.1c Oblique Loading:

In real impact events, most of the structural components, however, will be subjected

to oblique loading. In recent years, investigations have therefore turned there attention to

examining the crush response of thin walled tubes under an oblique load. The investigations

of the oblique crush response of square tubes was pioneered by Han and Park (1999) of

particular concerned in the study was the effect of the load angle on the mean crush load.

Compared with the load angle, the effect of geometry parameters such as wall thickness and

tube width on the tube response is negligible. Overall, the experimental results showed that

the mean load under an oblique load drops to about 40% of the mean crush load under pure

axial loading, at a critical load angle (transition angle from progressive crushing to global

bending) due to the formation of a bending collapse mode.

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Fig 3.2 Oblique crush phenomena of truck

Above fig 3.2 shows an impact event, especially vehicle crashes, the structure experiences

pure axial or pure bending load, rather it collapses in a complex manner under axial and non-

axial or oblique loads.

3.4.1d Dynamic Loading:

A dynamic load, on the other hand, causes a structure to vibrate and the inertia force

is big enough and must be considered. Impact involves a load quickly applied over short time

duration. High velocity impact means that it happens so fast that deformation barely develops

during such short time duration and hence fracture occurs.LS-Dyna deals with high velocity

impact.

3.5 Types of Analysis:

The energy absorbing tubes can be analyzed by two ways,

1. Experimental Analysis

2. Software Analysis

3.5.1 Experimental Analysis:

Quasi static loading test can be tested using standard universal testing machine.

Quasi-static test are convenient for analyzing energy absorber response since they allow

continuous monitoring of load, displacement and deformation mode. A screw type Tinius

Olesen universal testing machine (shown fig 3.3) is used for all quasi static tests.

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Fig 3.3 Tinius Olesen universal testing machine

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3.5.2 Software Analysis:

There are explicit non-linear finite element (FE) codes that implement numerical

studies for dynamic crush response of energy absorbers, Such as LS-DYNA3D, ABAQUS,

and LS-DYNA. But most researchers prefer LS-DYNA for software analysis. The main

typical applications of LS-DYNA are crash and vehicular simulations, impact analysis, metal

forming and drop tests. The ability of LS-DYNA to treat various contact algorithms for

different materials is anticipated to be highly useful in the design and analysis of the tubes.

Main areas of application

The numerous features of LS-DYNA enable the software to be employed in many

different fields. A list of common applications is given below,

Crashworthiness simulations of automobiles, trains, and ships

Emergency airplane landings

Occupant safety analysis

Pedestrian safety analysis

Automotive parts manufacture

Car bodies:

-Seats

- Roofs

- Doors

- Hoods

- Bumpers

- Crash boxes

- Girders

- Steering wheels

- Steering columns

- Dash-boards

- Padding

Metal forming:

- Rolling

- Extrusion

- Forging

- Casting

- Spinning

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- Ironing

- Superplastic forming

- Sheet metal stamping

- Profile rolling

- Deep drawing

- Hydroforming

- Multi-stage processes

- Spring back

- Hemming

Metal cutting

Glass forming

Biomedical applications

Stability/failure investigations

Drop tests

- Consumer products

- Nuclear vessels

Earthquake engineering

Bird strike

Jet engine blade containment

Penetration

Plastics, mold, and blow forming

Blast loading

Spot welded, riveted and bolted structures

Shipping containers

Can and container design

LS-DYNA is a highly advanced general purpose nonlinear finite element program that is

capable of simulating complex real world problems. The distributed and shared memory

solver provides very short turnaround times on desktop computers and clusters operated using

Linux, Windows, and UNIX.

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Chapter 4

CASE STUDY

By carrying out finite element simulation, energy absorption values of thin-walled

tubes with different geometric dimensions were investigated. Square, circular, and elliptic

tubes of steel and aluminum were used to compare energy absorption. The experimental

results of load-displacement used for verification in the square steel tubes showed good

agreement. Three-dimensional simulation was accomplished with a finite element method

while the impact or collided with one side of tube and the other side was kept rigid. Square

tubes for 2 specified widths with 2 different thicknesses were also compared. In addition, 2

other cross sections including circle and ellipse with the same area were studied for

comparison in a load displacement curve. The results show that the ellipse cross section had

more energy absorption than the 2 others. Moreover, the amount of energy absorption will be

greater with increasing thickness for smaller section tubes.

4.1 Observation Parameters:

In the laboratory test, load, displacement and rotation of jack were measured and the

following response parameters were obtained based on these measurement.

Peak force

Absorbed energy

Mean (crush) force

Deformation mode

4.1.1 Peak force:

The peak force is the maximum of the force displacement curve related to the

formation of the first local buckle in the column i.e. it appears in the initial phase of the test.

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Fig 4.1 Force verses displacement

Mathematically it is calculated as F = M x V / t kN where M=mass, V=velocity, t = per unit

time.

4.1.2 Absorbed energy:

Absorbed energy is the area under the force deformation curve for the current

deformation of the column. As it is shown in fig 4.1 mathematically it is calculated as,

4.1.3 Mean (crush) force:

Mean (crush) force is defined as absorbed energy divided by the current deformation

of the column.

Fig 6.3 mean force verses displacement

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Mathematically it is calculated as,

Where, {∫ ( )

}

b= breadth of the tube

h=height of the tube

4.1.4 Deformation Mode:

The deformation mode is a mode qualitative measure of the deformation pattern of the

column that is observed after the test, where detailed observations of local buckling, plastic

folding and fracture are reported.

4.2 Comparative of different tubes:

The comparison between three different tubes is carried out with above said

parameters. The table 4.1 shows this comparison, where the tubes are made of different

materials such as aluminum and steel.

Table 4.1 Energy and mean force comparison

Group

Circle Square Ellipse

Eabsorbed Fmax Fmin Eabsorbed Fmax Fmin Eabsorbed Fmax Fmin

(j) (kN) (kN) (j) (kN) (kN) (j) (kN) (kN)

Steel 3915 78.06 46.8 3406.5 66.1 36.2 5206.95 98.78 44.45

Aluminum 870 50.04 38.4 757 48.6 28.5 1157.1 70.035 40.8

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4.2.1 Load-Displacement curves:

Fig 4.1 and 4.2 shows that the Load-Displacement of square, circle and elliptic steel

tubes and aluminum tubes respectively.

Fig 4.1 Load-Displacement of square, circle and elliptic steel tubes

Fig 4.2 Load-Displacement of square, circle and elliptic aluminum tubes

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4.3 Modeling:

In this study, for modeling and simulation we are going to use following software’s

LS-DYNA

ANSYS

LS-DYNA is employed to investigate the deformation of tubes under dynamic

loading conditions. Some various choices of impact element can be considered like implicit

and explicit models. Here nonlinear explicit impact modeling elements are used for analysis.

Fig 7.1 three-dimensional model

The tubes used are of different widths and thickness but fixed lengths with three dimensional

models as shown fig 7.1. ANSYS software with an element type of thin shell element is used

for modeling and LS-DYNA software for analysis. By finite element simulation, energy

absorptions of different tubes can be investigated.

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Chapter 5

CONCLUSION

In this seminar axial crushing of steel and aluminium tubes between two parallel

plates subjected to impact dynamic axial and oblique loading were studied. A nonlinear finite

element model was developed and analyzed with LS-DYNA in this simulation. Typical

deformation histories for three sectional types (square, circle, ellipse, hexagon, octagon,

triangular) were studied and presented. It is concluded that elliptic tubes absorbed more

energy during collisions. The effects of width and thickness were also studied. It is concluded

that energy absorption may be increased about 22% with width enhancement of 66%,

showing that the energy absorption will be more with increasing thickness for smaller section

tubes. Energy per weight absorption during the collision of two metals (steel and aluminium)

is also studied and compared. The study showed that the amount of energy absorption per

weight of steel tube is about 4.5 times greater than the aluminium tube for all three sections,

square, circle and ellipse. However the square section and then the circular section of the

steel tube absorbed energy per weight more than the elliptic section of the aluminium tube. A

comparative study showed that multi-cell sections have greater specific absorption of energy,

in comparison with simple section especially for triangular geometry.

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Chapter 6

REFERENCES

1. Javad Marzbanrad, Mehdi Mehdikhnlo, Ashkan Saeedi Pour “An energy absorption

comparison of square, circular, and elliptic steel and aluminum tubes under impact

loading” ,2009.

2. A.AlaviNian,M Parsapour “Comparative analysis of energy absorption capacity of

simple and multi-cell thin-walled tubes with triangular, square, hexagonal and

octagonal sections”,2013.

3. T Bovik,O S Hopperstad, A Reyes, M Langseth, G Solomosnad T Dyngeland “Empty

and foam filled circular aluminium tubes subjected to axial and oblique quasi static

loading”, 2003.

4. Md. Reyaz Ur Rahimí A.K. Upadhyay K.K. Shukla “Energy absorption by circular

tubes subjected to oblique loading”, 2014.

5. Yong Zhang, Guangyong Sun, Guangyao Li , Zhen Luo , Qing Li “Optimization of

foam filled bi-tubal structures for crashworthiness criteria ”, 2012.

6. Abramowicz, W. and Jones, N., “Dynamic Axial Crushing of Square Tubes”, Int. J.

Impact Eng., 2, 179-208, 1984.

7. Aljawi, A.A.N., Abd-Rabou, M. and Asiri, S., “Finite Element and Experimental

Analysis of Square Tubes under Dynamic Axial Crushing”, European Congress on

Computational Methods in Applied Sciences and Engineering, 2004.

8. Babbage, J.M. and Mallick, P.K., “Static Axial Crush Performance of Unfilled and

Foam-Filled Aluminum–CompositeHybrid Tubes “, Composite Structures 70, 177-

184, 2005.

9. DiPaolo, B.P., Monteiro, P.J.M. and Gronsky, R., “Quasi-Static Axial Crush

Response of a Thin-Wall, Stainless Steel Box Component” International Journal of

Solids and Structures 41, 3707-3733, 2004.

10. Hanssen, A.G., Langseth, M. and Hopperstad, O.S., “Optimum Design for Energy

Absorption of Square Aluminum Columns with Aluminum Foam Filler Structural

Impact”, International Journal of Mechanical Sciences, 43153-176, 2001.

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ABSTRACT